Teaching Reflective Commentary Portfolio Mathematics

Teaching Reflective Commentary Portfolio

Mathematics is an area of education not often sought after by those teachers interested in true education. The subjects typically seem dry and students rarely take the courses seriously. In the field of accounting, however, there has been a much larger deficiency in properly educating students. As stated by Rob Gray (2006), in his article,

There is evidence that accounting education fails to develop students' intellectual and, relatedly, ethical maturity. This, it can be argued, may be seen as a moral failure on the part of accounting educators. This, it can be argued, may be seen as a moral failure on the part of accounting educators. The content of much of what currently passes for core accounting knowledge has characteristics which can be associated with both superficial learning strategies and ethically immature moral positions. Thus, it may be that 'current accounting knowledge' implicitly reinforces accounting education.

It is this premise that leads me to believe that there are methods that can be used to aid in both student learning and enjoyment. Through understanding the material and realizing the possibilities, a teacher can help his students look beyond the simple fact that they are in a statistics or accounting course and instead see the big picture of what their education will accomplish once they enter the real world. It is this premise that leads me to propose a different way to teaching these college courses that appeals to all learning styles while still teaching the essential knowledge.

Teaching Techniques and Student Memory Retention

As a student enters the accounting field and begins their education through a university, they are introduced to many new mathematical concepts and may feel overwhelmed from the start. There are many first year instructors who prefer simply lecturing as their form of educating students and expect the students to retain or remember the information for an exam. The problem with this approach is that it only scratches the surface of education and will not benefit the student after they complete their education and must apply what they've learned in the real world. In fact, according to Bloom's taxonomy, simply remembering and even understanding certain complex topics is merely the tip of the iceberg within the educational system.

Categories in the cognitive domain of Bloom's Taxonomy (Anderson & Krathwohl, 2001)

It is this lack of real application and an abundance of knowledge of theoretical concepts that is resulting in many accountants not being able to function once they leave the university. Igor Batista (2005) argues:

It is evident that we need to rethink business education, updating all the means to current needs. This model bears not only the components of a qualification system to accountants- including techniques, skills and desirable values required for the graduation, but allows the contents that should be considered as a guide in order to prepare and organize a program in tune with the global needs within the field. (22)

In order to move a student to success in the field of accounting, that student must be able to properly analyze the information given in school so that it can be used in the real world where word problems are no longer created to correlate to specific issues and it is clients who are looking to that student for help and advice. According to Bloom's taxonomy, this higher point of comprehension is achieved when a student can "Examine and break apart information into parts by identifying causes. The student can also make inferences and find evidence that supports generalizations." (Anderson & Krathwohl, 2000).

Moving an accounting student to this higher level of thinking is the most advantageous goal that a professor can strive for. In fact, studies have shown that those students capable of critical thinking receive much greater acceptance in their field after graduation. According to a study conducted by Robert Rademacher (1999), the more students were able to critically analyze information from various schools, the higher their acceptance rate of papers for publication.

The issue now turns to whether it is possible to take a student to this level of comprehension within the framework of accounting education. The answer is simply, yes. This is entirely possible when using the proper techniques within the classroom. While formal lecture has its place, it cannot be the only technique used. Rather, an integrated approach must be taken within the classroom setting in order to encourage students to move to that final level of comprehension and improvement. This paper will discuss the essential components which move an accounting student beyond simply remembering information by discussing, cooperative learning techniques, proper study habits, micro teaching strategies and examples, and strategies to guide every learning style through the material.

Moving Beyond Remembering

Rote memorization has its place within the education setting. It would be impossible for a student to master calculus if he did not memorize the basic rules of derivatives and integrals. However, once the concepts are memorized, a student must be able to do more than simply recite the rules. Instead, a student must learn how to look at the rules from different angles and apply those rules to various circumstances. This is the level of comprehension known as critical thinking (Duron, 2006). While most consider critical thinking to fall within the realm of the language arts, it is also an important aspect of accounting. According to authors Duron, Limbach, and Waugh, there is a five-step framework for implementing critical thinking within the field of accounting.

The first step to creating a critical-thinking-based lesson is to determine the learning objectives. The objective should never be vague or unclear, but rather focused on the particular behaviors or actions desired of the students (Duron, 2006). For instance, in a lesson on forecasting, the desired objective would be for students to identify all necessary components to form an accurate forecasting report and explain why each factor is necessary as well as those that are not. This goal may sound simple, but mastery of the skill can be difficult and elusive to most students. So, this goal must be kept consistent throughout the lesson. One important factor for keeping this goal consistent is to ensure proper primary and secondary sources of information for the students to review and utilize (Nentl, 2008). Given that each forecasting scenario is different, a student must have enough resources and knowledge to understand that thinking outside of the box is required. The objective must hit on each level of the Bloom's taxonomy via questions addressed to students. According to Duron, examples include:

Knowledge level requires an answer that demonstrates simple recall of facts. Questions at this level could ask students to answer who and what and to describe, state, and list. Comprehension requires an answer that demonstrates an understanding of the information. Questions at this level might ask students to summarize, explain, paraphrase, compare, and contrast. Application requires an answer that demonstrates an ability to use information, concepts and theories in new situations. Questions at this level may ask students to apply, construct, solve, discover, and show. Analysis requires an answer that demonstrates an ability to see patterns and classify information, concepts, and theories into component parts. Questions at this level could ask students to examine, classify, categorize, differentiate, and analyze. Synthesis requires an answer that demonstrates an ability to relate knowledge from several areas to create new or original work. Questions at this level might ask students to combine, construct, create, role-play, and suppose. Finally, Evaluation requires an answer that demonstrates ability to judge evidence based on reasoned argument. Questions at this level may ask students to assess, criticize, recommend, predict, and evaluate. (162)

So, the objectives should have enough flexibility and contour to ensure all forms of questions are asked and presented for the students to practice.

The next step, according to Duron is to "Teach through questioning." This method, also known as the Socratic method has been utilized by teachers since the time of the ancient Greeks to foster critical thinking (Smith, 1987). In the field of accounting ethics, this method has taken on a new form known as the "Case Method" in which students are asked to role play or evaluate basic cases or problems and determine what should be done in each case (Shugan, 2006). This method can also be applied to statistics. For instance, in the above forecasting model, instead of simply working out an example problem and moving on, a teacher desiring critical thinking skills will change the variables within the problem and force the students to come at the problem from new angles. This probing does not end until the student is adequately able to see past the simple rules and procedures and apply the principles. According to Duron, there are different forms of questions that can be brought into the analytical process:

Questioning techniques can be used to foster the thinking ability of students. Questions can be categorized in a number of different ways. One simple method is to use the general categories of convergent and divergent questions. Convergent questions seek one or more very specific correct answers, while divergent questions seek a wide variety of correct answers. Convergent questions apply to Bloom's lower levels of Knowledge, Comprehension, and Application

and may include questions like "Define nutrition," "Explain the concept of investing," and "Solve for the value of X." Divergent questions apply to Bloom's higher levels of Analysis, Synthesis, and Evaluation; are generally open-ended; and foster student-centered discussion, thereby encouraging critical thinking. For example, "Describe the qualities that make a person successful," "Create an office design to facilitate group interaction," and "Describe how sun spots might affect tree growth" are all divergent questions. (162)

So, not every question even needs to lead the students through the same pathway. In the above example, a false-factor could be thrown into the mix, simply to force the student out of any developing routine when analyzing the problem.

The third suggested step to bringing about critical thinking in accounting is to have the students practice various techniques before assessing those techniques. Fink (2003), a leading educational writer, addresses this by creating two steps to consider when creating preparatory learning activities:

First, activities should be chosen from each of the following three components of active learning: Information and Ideas, Experience, and Reflective Dialog. Information and Ideas include primary and secondary sources accessed in class,

outside class, or online; Experience includes doing, observing, and simulations; Reflective dialog includes papers, portfolios, and journaling. Second, whenever possible, direct kinds of learning activities should be used. Examples of direct activities include doing in an authentic setting, direct observation of a phenomenon, reflective thinking, service learning, journaling, and dialog in or outside of class.

The key is to select an activity that fits the lesson and the teacher's teaching preferences. For example, when teaching forecasting in a college level setting, a trip to the math computer lab and working with a forecasting program would allow the students the opportunity to practice the skills in a more realistic and less theoretical setting.

Computer simulation programs have become the ultimate in helpfulness in giving students a realistic application. According to a study conducted by Igor Batista and Edgard Cornachione (2005), the following results were achieved once students began using a business simulation program:

As can be seen, when the students used the program, their overall comprehension and application skills improved by roughly 50% in every area. In fact, by the end of the simulation, 81% of students were able to create other types of business applications. It is this ability that will allow the students to stand out and perform well in the real world.

Step four is by far the most vital to true quality teaching, and will be further addressed later in this essay in greater detail. This step is to review, refine, and improve a course. Courses should never be stagnant, but rather through the use of constant reflection and student surveys be improved and updated. According to Duron:

Teachers should strive to continually refine their courses to ensure that their instructional techniques are in fact helping students develop critical thinking skills. To accomplish this, teachers should monitor the classroom activities very closely. To track student participation, a teaching diary can be kept that identifies the students that participated, describes the main class activities, and provides an assessment of their success. Other reflective comments can also be tracked in this journal and can be very useful when revising or updating instructional activities. (163)

Along with journaling, another very powerful tool to ensure the course is teaching critical thinking is through student surveys. While some students may be put off by being forced to do more than simply listen to lectures, others will give honest feedback at how the activities assisted in further understanding the material being taught. Furthermore, the surveys need not be given in a survey form. Angelo and Cross (1993) suggest using indirect techniques such as giving students a two-minute paper where they are asked to identify the most important points learned within a certain lesson.

The final step to creating critical thinking in any skill, including accounting courses, is to provide feedback to students through assessment. Even though the simpler approach, and an understandable one given class sizes, is to assign a certain number of problems, mark the incorrect problems, and move on to the next paper, this does not offer the students a chance to reflect or improve. During my time as a student, I have had the opportunity to tutor multiple entry level accounting students and the one area that most are lacking is feedback. The students strive to improve in the course, but do not understand how. Thankfully, tutors have much more time to devote to feedback and can offer the necessary advice and guidance that a busy professor cannot. A simple way for teachers to start offering feedback is to use more word problems or problems with extended analysis. Encourage the students to write out all steps so that you can correct any and all incorrect steps while grading as a means of pointing the student back into the right direction.

Teaching Techniques

While preparing lessons, teachers should also come to grips with the reality that simply standing in front of a classroom will not merit a very responsive or well-informed class. Even more so, simply teaching out of a textbook will not ensure proper learning. Instead, instructors should integrate the lecture approach with a small group interval offered. For instance, a professor could lecture for the first class during the week, and end the lecture giving the students further reading for the following lesson and an extended word problem. During the next class, the instructor selects students to verbally work out the word problem with the guidance of the instructor at the board. Finally, the third session for the week is with smaller groups of students meeting with student aids and working on problems that extend slightly outside of the box of the textbook lesson, allowing the students to apply the principles in a different way. This example of teaching style is becoming more widely adopted by many universities as a means of ensuring that accounting students are prepared for the real world (Ainsworth, 1994). As can be seen, within a single week's worth of course lessons, students are taken entirely through the Bloom's Taxonomy and will reach the final desired stage.

This technique may seem overly complex or difficult to employ in the classroom, however, textbooks are now integrating Bloom's taxonomy in order to encourage use by professors. In a paper written by Ronald Davidson and Bruce Baldwin (2004), it was found that between the years of 1934 and 2004, the problems at the end of chapters have consistently went through the various components of Bloom's taxonomy, even before his published theory emerged. In other words, a properly prepared professor need only utilize the material at the end of each course chapter in order to ensure that the goals of Bloom's taxonomy are reached by his students.

Microteaching

The greatest improvement by which a teacher can make to their curriculum is through self-reflection and improvement. One technique that many professors are using to improve their teaching style and approaches is microteaching (Jiannong, 2002). The first step in this approach is to videotape ones self teaching a class. Often there is no greater critic of ones work than ones self and many mistakes can be caught and corrected by simply reviewing the tape. The next step is to be critically reviewed by a peer or professor. While every teacher's learning style is different, seasoned teachers can offer excellent advice that will assist in improving overall teaching style. A critical review by a teacher does not need to be long or time consuming, but can rather ask some very basic questions. Below is an example of a teaching review from one of my own lessons:

As can be seen in the image, the observer is an established professor. The evaluation does not simply address speaking and presentation style, but also the response of the students and the comparative quality and effectiveness of the teacher's overall objectives. In this example, improvement was suggested with regard to the methods of having the students complete problems on the white board. Instead, it is recommended to have the students complete the problems in groups. Whereas videotaping ones self will produce an improvement in overall presentation, it is these evaluations that will improve the overall quality and effectiveness of the lessons.

Intended Learning Outcomes in Accounting

It is an established fact that there is a learning gap with accounting students (Baker, 1987). Students leave accounting with only basic knowledge of the theories and are typically unable to effectively evaluate and process problems in the real world. This lack of flexibility is caused directly by a lack of higher thinking objectives within the classroom setting. In order for teachers to ensure their students reach that higher level of analytical ability, the framework must be established in advance and objectives reached. Duron presents the precise analysis and argument in his article:

Basic financial statement analysis is a skill taught in most introductory financial accounting courses. It represents a good example of a skill that is built upon in other business courses (i.e., finance, business strategy) and is also likely to be utilized by most business professionals. The first step in the model (Determine Learning Objectives) involves the determination of behaviors students should exhibit appropriate to the various levels of Bloom's taxonomy as shown in Table 1.

Note that the development of these objectives not only provides for increasingly higher levels of learning (those which demonstrate critical thinking), but also provides a basis for developing appropriate questions, designing specific learning activities, and giving feedback on and assessing student learning outcomes.

The next critical step in the model (Teach through Questioning) is to develop questions (based upon the learning objectives identified above) and prepare to employ appropriate questioning techniques that help foster an active learning environment. In this context, the use of both focused and open discussion formats is recommended. Convergent questions are utilized to assist students in mastering the basic financial analysis concepts (i.e., knowledge, comprehension, and analysis), while divergent questions are proposed for the learning outcomes identified above which may include a variety of correct responses (i.e., analysis, synthesis, and evaluation). In accounting in particular, it may be necessary occasionally for the instructor to digress to the lecture format to explain difficult concepts or computational nuances. Nonetheless, a concerted effort should be made to keep the students actively and equally engaged.

In implementing Step 3 of the model (Practice before You Assess), working through the objectives and questions can be accomplished using a variety of activities. For this particular topic, students might be given a reading assignment and then administered a short reading quiz at the beginning of class to provide both practice and feedback on the knowledge and comprehension aspects of the topic. Once the teacher is reasonably sure that the students are able to perform the analysis and compute the ratios correctly, students may be placed in teams to perform the actual analysis of the statements. For higher levels of learning, the guidelines of Fink (2003) can and should be followed. For example, students might be asked to utilize information from real companies by accessing financial statements online and then using the data to compute ratios either in groups or individually in a real world application. Students may be asked to critique the analysis, synthesis, or evaluation of others. At the conclusion of class or the learning unit, a useful exercise in this setting is that of a reflective journaling activity. For example, students might be asked to reflect in writing upon "how what I learned will be of use to me in my chosen profession." In addition to encouraging students to reflect upon what they have actually learned, this type of activity also helps make the material personally and/or professionally relevant. (163-4)